The Social Democrats, led by Aksel Johannesen, gained two seats in the autonomous territory's 33-member parliament and are expected to form a new government with the pro-independence Republic party.
Their coalition will have to include at least one out of two smaller centrist parties to have a parliamentary majority.
The new government is expected to pass legislation allowing same-sex unions.
While its former colonial master Denmark was the first country in the world to recognize same-sex unions in 1989 and legalized gay marriage in 2012, the issue has been controversial in the deeply-religious Faroes.
The main political parties have allowed their lawmakers to take their own positions on the subject, but Gestur Hovgaard, a social sciences researcher at the University of the Faroe Islands, said the left-wing government would probably now have enough votes in parliament to introduce same-sex unions.
Meanwhile, the ruling coalition's two main parties, the conservative-liberal Union Party and the pro-independence People's Party, each lost two seats after an election campaign that had also focused on taxing the booming fisheries sector and tax cuts that the opposition claimed had undermined public finances.
"There was a sharp line between the opposition and the government on central issues like fisheries policy and taxation," Hovgaard said.
Prime Minister Kaj Leo Johannesen called the election on July 29 after being embroiled in controversy when a probe found that he lied to parliament about a contract to build a subsea tunnel between two islands.
The Faroe Islands are not part of the EU and salmon exports to Russia have soared after Moscow last year slapped a ban on food products from the bloc.
The opposition has argued that fishing firms, whose sales account for up to 98 percent of the debt-laden territory's exports, should contribute more to the public purse.
The archipelago, with 48,000 inhabitants and around 70,000 sheep, has been autonomous from Denmark since 1948 -- although foreign affairs and defence are still the domain of Copenhagen.